BRASILIA—Brazil's Supreme Court voted Wednesday to reassess the landmark convictions it handed down against a dozen defendants found guilty last year of participating in a vote-buying scheme that rocked the government of former President Luiz Inácio Lula da Silva.

The 6-5 vote allows 12 of the 25 defendants in the case, including Mr. da Silva's once-powerful chief of staff José Dirceu, to appeal parts of their prison sentences, which...